An atomic frequency standard is a device having a resonant system derived from an atomic or molecular specie experiencing a transition between two or more well-defined energy levels of the atom or molecule.
For example, the two lowest energy levels of the rubidium atom (Rb) are known as the ground state hyperfine energy levels A and B. When atoms of gaseous Rb-87 at levels A and B are interrogated (irradiated) with microwave energy at a precise "transition frequency", corresponding to the rubidium frequency representing atom transitions between the hyperfine energy levels, the rubidium atoms at hyperfine energy level A will make the transition to level B, and vice versa. The transition is employed as a highly accurate frequency reference to which the frequency of a frequency controllable oscillator, such as a voltage-controlled crystal oscillator (VCXO), can be electronically locked in creating an atomic frequency standard.
In such atomic-controlled oscillators the frequency of a quartz crystal oscillator is controlled by means of a physics package and associated electronics that are devoted to maintaining the assigned output frequency, typically 5 MHz or 10 MHz, on a very long-term, exceedingly accurate and stable basis. By properly slaving a quartz crystal oscillator to the frequency of the atomic transition in the physics package, the tendency of the quartz crystal to exhibit drifting due to aging and other inherent as well as environmental effects is markedly suppressed. The physics package of a typical atomic frequency standard generally includes a microwave cavity resonator, an isotopic filter cell, an absorption cell, a light source, a photo detector, temperature control means, at least one magnetic shield surrounding these components, and a C-field coil.
In the physics package of a typical rubidium atomic frequency standard 10, as for example shown diagrammatically in FIG. 1, a light source 11 includes a glass bulb containing rubidium atoms which produces light by an rf-excited plasma discharge. The rubidium in the lamp 11 is heated to a vapor state, approximately 110.degree. C., and is subjected to a high-energy rf field, thereby generating light from the excited rubidium atoms. The "rubidium light" is directed through a filter cell 25a which contains an isotope of rubidium, such as Rb-85, which filters out light with a wavelength that will stimulate transition of atoms from the hyperfine energy level B to any optically-excited level C. The filtered rubidium light is then directed through an absorption cell 25, also called a resonance cell. The absorption cell 25 includes another isotope of rubidium, Rb-87, and the filtered light energy absorbed by the Rb-87 atoms at hyperfine energy level A causes a transition of the Rb-87 atoms from level A to an optically-excited energy level C. The atoms excited to energy level C, however, do not remain at level C for more than tens of nanoseconds, but return to ground state hyperfine levels A and B in approximately equal numbers by either spontaneous emission of light and/or by collisions, including collisions with other atoms, molecules, or the walls of the absorption cell 25. Since the filtered light does not allow transitions of atoms from level B to level C, the continuing cycle of optical excitation of atoms from level A to level C and the redistribution of atoms falling from level C between levels A and B eventually results in few, if any, atoms at level A for excitation to level C, and little or no absorption of the light passing through the absorption cell 25 because the atoms have accumulated at hyperfine energy level B. The atoms at level A are said to have been "optically pumped" level B. If, however, microwave energy is applied to the absorption cell 25 at the rubidium transition frequency, transitions of atoms between hyperfine levels A and B occur, re-introducing atoms at level A which again absorb light energy and undergo a subsequent transition to level C and thereby reduce the light passing through the absorption cell 25.
The rubidium light passing through the absorption cell 25 is incident on a photo detector 16, which produces a current output which is proportional to the intensity of the incident light. The current output is processed to provide a control voltage to a voltage controlled crystal oscillator 27 (VCXO) (not shown in FIG. 1) whose output is multiplied and synthesized to the rubidium transition frequency and provides the microwave energy used to cause the transitions between hyperfine levels A and B. When the frequency of the microwave energy corresponds to the hyperfine transition frequency, 6.834 GHz for Rb-87, maximum light absorption occurs and the current output of the photo detector 16 is reduced. If, however, the frequency of the microwave energy does not correspond to the hyperfine frequency, then more light will pass through the absorption cell 25 to the photo detector 16, which in turn increases its current output. Thus, as shown in FIG. 1, the light intensity at the photodetector 16 is at a minimum when the microwave energy from the VCXO 27 is at the hyperfine frequency.
During the last several years attention within the time and frequency community has been directed to efforts to develop frequency sources having exceptionally high short-term frequency stability for use as "flywheels" for the next generation of ultra-long-term stable frequency standards, such as ion storage standards. One of the limitations to improving short-term stability (STS) in passive atomic frequency standards is the phase noise in the frequency source that interrogates the atoms.
All passive atomic frequency standards use modulation methods to lock the interrogation frequency to the more stable atomic reference frequency. Of special concern with the use of a frequency modulated interrogation signal is the phase noise of the interrogating signal that occurs at a Fourier frequency (offset from the carrier frequency) equal to two times the modulation frequency (2f.sub.mod).
The interrogating signal, including modulation, can be represented by a carrier at the interrogating frequency (which is nominally equal to the frequency of the atomic resonance) plus sidebands of various amplitudes spaced at intervals equal to the modulation frequency. The carrier plus sidebands act as a stimulus for the atoms that provide the frequency reference for the standard. The atoms and the physics package of the standard provide a response to this stimulus in the form of a modulated signal that is processed by an electronic servo system of the atomic standard to slave the VCXO frequency to the resonance frequency of the atoms. The strength of the output signal of the physics package depends on how strong the atom response is to the stimulus which is based, at least in part, on the positions of the carrier and sidebands within the atomic bandwith (ABW). In assessing this effect, the carrier and each sideband must be considered individually, according to the superposition principle.
The physics package output signal results from a mixing effect whereby the various sidebands and the carrier, each suitably modified by the atomic response, beat against each other in the photodetector producing various sum and difference frequencies. The sum frequencies are not of interest and can be ignored. The difference frequencies are equal to the modulation frequency and the harmonics of the modulation frequency.
It is well known that a second harmonic component in the modulating frequency produces an unwanted signal at the physics package output at the modulation frequency. The electronic servo system cannot distinguish this "pseudo" error signal from a true error signal and therefore produces an offset in the output frequency of the standard in order to null this signal at the input of the servo integrator. Thus, second harmonic contamination in the modulating signal produces an offset in the standard's output frequency. Likewise, the presence of phase noise at 2f.sub.mod in the interrogating signal causes the physics package to produce an output noise component at frequency f.sub.mod ; in effect, the physics package acts as a phase noise-to-amplitude noise convertor with down conversion from 2f.sub.mod to f.sub.mod. The f.sub.mod noise component is demodulated by the servo to produce low frequency phase noise on the standard's output. This low frequency phase noise degrades the standard's STS.
Phase noise of a frequency modulated interrogating signal can thus be important in limiting the STS of a compact commercial atomic frequency standard. If a poor quality VCXO is used to generate the interrogation signal in an atomic frequency standard, the phase noise and associated sidebands may limit the STS to higher than normal values. Alternatively, if the desired STS goal is lower than normal, the phase noise may be limiting, even with a good VCXO.
Even when a good VCXO is used, the method of generating the interrogating signal may introduce additional phase noise that limits the STS. For example, in a rubidium frequency standard, this would include the use of a multiplier chain consisting of a 360 MHz VCO that is phase locked to a 10 MHz VCXO, with the output of the 360 MHz VCO multiplied to 6840 MHz by a step recovery diode (SRD). Even though the VCXO has relatively low phase noise, the free running VCO does not. Tight phase lock of the VCO is desirable in this scheme to reduce the VCO phase noise by slaving it to the lower-phase-noise VCXO. If the lock is not tight enough, the "residual" phase noise of the VCO may affect the STS of the standard.
Audoin and coworkers have developed a theory to account for such phase noise using quasi-static modulation theory. See A Limit to the Frequency Stability of Passive Frequency Standards Due to an Intermodulation Effect, IEEE Trans. Instr. Meas. 40, 121 (1991). Unfortunately, this theory is valid only in the limit where the modulation frequency is significantly smaller than the atomic linewidth (bandwidth), namely, f.sub.mod &lt;&lt;ABW, where ABW=atomic bandwidth=full width at half maximum signal of the atomic line.
Experimental tests of the theory have been conducted. Walls and coworkers have demonstrated a method for improving STS by using a dual crystal notch filter to remove phase noise at .+-.2f.sub.mod from the interrogation frequency. See Reducing Local Oscillator Phase Noise Limitations on the Frequency Stability of Passive Frequency Standards Tests of a New Concept, IEEE Trans. Ultrasonics, Ferroelectrics & Freq. Control 41, 518 (1994). However, the dual crystal filter method of reducing interrogation phase noise is complex and costly and therefore, is not practical in passive, compact, low-cost commercial atomic standards.
Notwithstanding the limited validity of the quasi-static modulation theory, it appears that all of the work done to date on phase noise reduction operates within the quasi-static paradigm where the modulation frequency is kept small compared to the atomic bandwidth (ABW) as illustrated in FIG. 3. By way of example, a passive, gas-cell rubidium standard has an atomic bandwidth of 700-1000 Hz, depending on various factors, including the strength of the interrogating signal, and conventional modulation frequencies are on the order of 100-130 Hz.
A need exists for a simple and economical method of reducing interrogation signal phase noise in passive, compact, low-cost commercial atomic standards, particularly phase noise occurring at a Fourier frequency equal to twice the modulation frequency, 2f.sub.mod.